Why Is It Harder to Rotate A Rod with a Mass in the Center?

  • Thread starter Thread starter sagebum
  • Start date Start date
  • Tags Tags
    Inertia
Click For Summary
SUMMARY

The discussion centers on the difficulty of rotating a rod with a mass (m1) at its center compared to a rod with two masses (m2) at its ends, with the condition that m1 equals 2*m2. Participants clarify that the rod with the mass at the center is indeed harder to rotate due to its moment of inertia. The relevant equations discussed include torque = moment of inertia x angular acceleration and Kr = I ω², which indicate that more work is required to achieve the same angular velocity for the rod with the mass in the center. Misunderstandings regarding the professor's explanation are also addressed.

PREREQUISITES
  • Understanding of rotational dynamics
  • Familiarity with moment of inertia concepts
  • Knowledge of torque and angular acceleration relationships
  • Basic proficiency in applying equations of motion for rotating bodies
NEXT STEPS
  • Study the concept of moment of inertia in detail, focusing on different mass distributions
  • Learn about the relationship between torque and angular acceleration in rotational systems
  • Explore the implications of the work-energy theorem in rotational motion
  • Investigate practical applications of rotational dynamics in engineering and physics
USEFUL FOR

Students studying physics, particularly those focusing on mechanics, as well as educators seeking to clarify concepts of rotational dynamics and moment of inertia.

sagebum
Messages
5
Reaction score
0

Homework Statement


Which is harder to rotate?
A rod with a mass (m1) in the center, or a rod with two masses (m2)at the ends.
Assume mass m1 = 2*m2, so the total masses of rod+masses are equal.
I am rotating the masses at the center.

My professor said that the one with the mass in the center is harder to rotate, but I don't understand how he explained it. I actually thought the one with the mass in the center was easier to rotate.

Can someone explain why the one with the mass in the center is harder to rotate?
Is it because if we were to rotate each to the same angular velocity, it would take more work to get the first rod to that angular velocity?

Relevant equations.
I think I'd use Kr = I \omega^{2}
and if they go up to the same angular velocities, it requires more work?
It doesn't seem right, because if the I of the first rod is lower, so the Kr would be lower, so that means the work required to get it to that speed was lower?
I don't see why the one with the mass in the center is easier to rotate.
 
Physics news on Phys.org
assuming that you are rotating about an axis that goes thru the center then it would harder to rotate the m2 case because it has larger moment of inertia. unless i have misunderstood the setup.
torque = moment of inertia x angular acceleration
you may have mis-heard your prof.. or there are something else in the system?
 
sagebum said:

Homework Statement


Can someone explain why the one with the mass in the center is harder to rotate?
Is it because if we were to rotate each to the same angular velocity, it would take more work to get the first rod to that angular velocity?

It wouldn't take any energy to rotate the rod with m1 in the centre, because the velo of the point mass at the centre would be zero.

Perhaps you misunderstood your professor, as mjsd says?
 
Yeah, I thought what u said was the answer too, I'll have to ask my professor again, maybe i switched up what he said.

Thanks for helping
 

Similar threads

Replies
10
Views
2K
  • · Replies 71 ·
3
Replies
71
Views
4K
  • · Replies 5 ·
Replies
5
Views
864
Replies
7
Views
2K
Replies
67
Views
4K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K
Replies
5
Views
1K
Replies
335
Views
16K
  • · Replies 13 ·
Replies
13
Views
2K